Lesson

# Clip 7/13: Calculating Volume of Rectangular Prisms Lesson Part 1F

## Overview

In the third act of the Three-Act Task, Mallory displays a still image, showing the box of sugar cubes disassembled so that the sugar cubes are revealed in a rectangular prism. Superimposed on the image are the dimensions: 3 x 6 x 11. Some of her 5th-grade students immediately start recording the new information. Mallory asks student groups to compare their estimates to this new information. Some observe that their estimates were wrong, and Mallory responds, “That’s not necessarily something we should be worrying about. It’s not about other groups; it’s about how we’re getting to the answer with our team.” She then distributes still images of each act and asks students to make the strategies they used in each of the three acts visible so that they can explain their reasoning.

## Teacher Commentary

Once we got past the second act and we started to show them the face or the layer, the first layer of the sugar cubes, some groups were able to reason through that there's multiple layers, and so they could create an estimate. If I think the height is 10, that means I'm going to have 10 layers. But oftentimes, a group would just use the 18, which was the total of the layer, so we had to go back and remind them that that layer was made up of a 3-by-6 array. So, when they drew their strategy to find the total amount of sugar cubes, they actually drew the 18 by 1 by 18. So going back to that group and explaining that if you're drawing 1 by 18, you're then changing the shape of the box. It'll get you the same solution, because you're trying to make the connection between how do I go from 18 to my final answer of 180 or 216; however, they then changed the dimensions of the box when they changed the array. I needed to make that connection that you cannot necessarily change the row by column, because that is the layer, the first layer that makes up the shape of that box.